Calculation of Combustion Explosion and Detonation

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98 S Grys W A Trzci ski, thermochemical codes for carrying out thermodynamic calculations of the. detonation parameters of condensed explosives for example a BKW Fortran 1. ARPEGE 2 Ruby 3 TIGER 4 CHEETAH 5 EXPLO5 6 MWEQ 7, BARUT X 8 Although in many research centers in the world thermochemical. codes were worked out access to them is difficult and moreover any changes in. the codes aren t possible because they are made available in the compiled form. Therefore at the Department of Explosives in the Warsaw Military University. of Technology decision has been taken to create own numerical code named. In Ref 9 the review of thermodynamic methods for determining the. equilibrium composition of complex mixtures was made These methods are used. in thermochemical codes to determine the combustion and detonation parameters. for energetic materials On this base the method for the determination of the. equilibrium and non equilibrium states for ideal heterogeneous systems was. proposed in Ref 10 and the computer program called ZMWI was applied for. calculation of the parameters of combustion and detonation of ideal explosives. compositions, In the work 11 the method of calculation of the equilibrium state of reacting. non ideal mixture and ways of application of this method for estimating the. parameters of combustion explosion and detonation of energetic materials were. described In addition procedures were proposed for calculation the JWL Jones. Wilkins Lee isentrope and the detonation energy on the basis of thermochemical. calculation results Moreover the method of non equilibrium calculations was. discussed in which the chemical inertness of one or a few components could be. assumed and no heat exchange between an inert compound and reaction products. could be supposed, In the present work the thermochemical program ZMWNI is described The. code can calculate the parameters of combustion explosion and detonation of. condensed energetic materials as well as determine the curve of expansion of. detonation products in the form of JWL isentrope 12 and the energy of detonation. 13 Moreover the ZMWNI code is able to determine the non equilibrium states. for frozen composition or for different temperatures of components. In the program ZMWNI the method based on the minimization of chemical. potential is applied to calculate the equilibrium or non equilibrium composition. of a reactive system The final collection of components is obtained through. solving the set of linear equations and the method of steepest descent 14. 11 Physical properties of gasses are described by the BKW equation of state. Becker Kistiakowsky Wilson For condensed components the OLD equation. of state applied in the thermochemical codes TIGER and CHEETAH is used. Calculation of Combustion Explosion and Detonation Characteristics 99. To determine the equilibrium state for combustion explosion in a fixed volume. or detonation of an energetic material the physical conditions appropriate for. the given process are taken into account These conditions are described herein. In the work the results of exemplary calculations are also presented To. verify the ZMWNI program these results are compared with that obtained from. the CHEETAH code In particular the outcome of determination of the adiabatic. combustion temperature JWL isentrope and detonation energy are shown. Moreover new possibilities of the program i e the non equilibrium calculations. are demonstrated At the end some experimental data are confronted with the. results obtained from the ZMWNI calculations,Equilibrium calculations.
Constant volume explosion, Conservation of the internal energy is a physical condition for a constant. volume explosion For this condition the temperature is an unknown state. parameter The aim of calculations is determination of the composition of. products for which the principle of conservation of internal energy is fulfilled. and the thermodynamic potential reaches its minimum. The results of constant volume explosion calculations are presented in Tables. 1 and 2 and they are compared with the values obtained from the CHEETAH code. The BKWC database 5 has been applied in the both programs Calculations. have been carried out for a loading density of 0 625 g cm3 The values of specific. enthalpy energy and entropy in Table 1 are relative given as changes from the. reactants state, Table 1 Comparison of the thermodynamic functions and parameters. obtained from the ZMWNI and CHEETAH codes for the constant. volume explosion of TNT,Pres Specific Tempe of,Enthalpy Energy Entropy. sure volume rature gaseous Code,cal g cal g cal K g. atm cm3 g K products,15801 1 6 2823 2 611 99 0 1 860 1 6 ZMWNI.
15806 1 6 2823 7 612 45 0 1 863 1 6 CHEETAH,100 S Grys W A Trzci ski. Table 2 Comparison of the products compositions obtained from the ZMWNI. and CHEETAH codes for the constant volume explosion of TNT. Contents mole moleExp Contents mole moleExp,Product Product. ZMWNI CHEETAH ZMWNI CHEETAH,CO 4 239E 00 4 239E 00 CH2O 8 209E 03 8 217E 03. N2 1 465E 00 1 465E 00 CH3 6 102E 03 6 111E 03,H2 1 243E 00 1 243E 00 C2H2 5 529E 03 5 538E 03. H2O 6 002E 01 6 002E 01 C2H6 4 846E 03 4 850E 03,CO2 5 690E 01 5 690E 01 CH2O2 4 650E 03 4 655E 03.
CH4 2 541E 01 2 541E 01 CHNO 2 748E 03 2 751E 03,NH3 4 165E 02 4 167E 02 H 1 830E 03 1 833E 03. CHN 2 584E 02 2 586E 02 CHO 1 211E 03 1 213E 03, C2H4 1 270E 02 1 271E 02 CH3OH 1 157E 03 1 159E 03. From the presented data it follows that differences between the values of. component quantity calculated by the both programs are less than 0 2. Combustion, For the adiabatic combustion at a constant pressure state the enthalpy of. a system should be constant during the process For an assigned pressure and. enthalpy calculations are aimed for seeking a minimum of the thermodynamic. potential In this way the so called adiabatic combustion temperature is. determined which is often used to characterize energetic properties of materials. The results of equilibrium calculations for exemplary mixtures containing. polytetrafluoroethylene PTFE and powder of magnesium are presented in Tables. 3 and 4 Calculations have been performed for a pressure of 1 atm The BKWS. database 15 containing compounds of fluorine and magnesium has been used. The enthalpy energy and entropy are calculated as changes from the reactants state. Table 3 Comparison of the thermodynamic parameters obtained from the. ZMWNI and CHEETAH codes for the adiabatic combustion of the. mixture containing 70 PTFE and 30 Mg,Pres Specific Tempe of. Enthalpy Energy Entropy,sure volume rature gaseous Code.
cal g cal g cal K g,atm cm3 g K products,1 4919 29 3696 69 0 119 11 1 595 4919 12 ZMWNI. 1 4919 30 3696 70 0 119 12 1 595 4919 26 CHEETAH, Calculation of Combustion Explosion and Detonation Characteristics 101. Table 4 Comparison of the products compositions obtained from the ZMWNI. and CHEETAH codes for the adiabatic combustion of the mixture. containing 70 PTFE and 30 Mg,Contents mole moleExp Contents mole moleExp. Product Product,ZMWNI CHEETAH ZMWNI CHEETAH,F2Mg 5 643E 01 5 643E 01 Mg 6 156E 03 6 156E 03. F 1 667E 01 1 667E 01 C2F2 3 755E 05 3 756E 05,CF2 1 746E 02 1 746E 02 C2 3 794E 03 3 794E 03.
CF 4 986E 02 4 986E 02 F2 1 524E 06 1 525E 06,FMg 6 752E 02 6 752E 02 C5 3 511E 04 3 511E 04. CF3 4 799E 05 4 801E 05 C2F4 1 524E 08 1 526E 08,CF4 1 798E 06 1 799E 06 C4 1 613E 04 1 613E 04. C3 2 753E 02 2 752E 02 C2F6 9 929E 13 9 943E 13, F4Mg2 3 296E 05 3 297E 05 C solid 4 726E 01 4 733E 01. Similarly to the constant volume explosion differences between the. contents values calculated for the constant pressure combustion by the use of. the CHEETAH and ZMWNI codes are small and they are below 0 2. Adiabatic combustion temperature K,3400 PTFE Al,3200 PTFE Mg. 0 10 20 30 40 50 60 70,Mass fraction of metal, Figure 1 Dependence of the adiabatic combustion temperature on the mass.
fraction of metal in PTFE Al and PTFE Mg mixtures,102 S Grys W A Trzci ski. The adiabatic temperature is very often used in numerical modeling of the. combustion process in solid energetic materials The option of the constant. pressure combustion in the ZMWNI code enable us to determine this parameter. for a chosen composition For example the dependence of the adiabatic. temperature on the mass fraction of a metal is presented in Figure 1 for mixtures. of PTFE with Mg or Al, Detonation parameters and isentropes of products expansion. To determine detonation parameters the relations resulting from the ideal. detonation theory are usually used From the equations of mass and momentum. conservation one can obtain the relation combining the detonation velocity. pressure and specific volume at the front of detonation wave the so called. Rayleigh line,v12 v 2 v1, where p1 1 denote the pressure and specific volume of an explosive p2 2 are. the pressure and specific volume of the reacting composition at the front of. detonation wave whereas D is a speed of propagation of the wave This equation. complete the equation of a detonation adiabate which connects p2 and 2 the. energy conservation equation According to the Chapman Jouguet hypothesis. the parameters p2 v2 at the point of tangency between the Rayleigh line and the. detonation adiabate curve are corresponding to the steady state detonation For. this point the detonation velocity D reaches a minimum This condition and the. principle of minimum of the thermodynamic potential are used to determine the. detonation pressure and the products composition After determining p2 and 2. other parameters of the detonation wave are calculated on the basis of commonly. known relations at the Chapman Jouguet point, The results of exemplary calculations for RDX density 1 63 g cm3 are. presented in Tables 5 7 The enthalpy energy and entropy are found as absolute. Table 5 Comparison of the RDX detonation parameters obtained from the. ZMWNI and CHEETAH codes,Detonation velocity Mass velocity Isentrope.
m s m s exponent,8267 2004 3 125 ZMWNI,8266 2005 3 123 CHEETAH. Calculation of Combustion Explosion and Detonation Characteristics 103. Table 6 Comparison of the thermodynamic detonation parameters obtained. from the ZMWNI and CHEETAH codes for RDX,Pressure fic Enthalpy Energy Entropy. rature gaseos Code,atm volume cal g cal g cal K g,K products. 266513 7 0 465 4259 9 3546 33 546 65 1 73 0 465 ZMWNI. 266578 7 0 465 4259 2 3546 64 546 52 1 73 0 465 CHEETAH. Table 7 Comparison of the products compositions obtained from ZMWNI. and CHEETAH codes for RDX,Contents mole moleExp Contents mole moleExp. Product Product,ZMWNI CHEETAH ZMWNI CHEETAH,N2 2 84E 00 2 84E 00 CNN 6 15E 11 6 12E 11.
CO2 1 98E 00 1 98E 00 N2O3 1 68E 11 1 68E 11,H2O 1 09E 00 1 09E 00 C3O2 7 21E 12 7 16E 12. CH2O2 4 22E 01 4 22E 01 C3 1 07E 12 1 06E 12,NH3 2 97E 01 2 97E 01 N2O5 7 49E 15 7 50E 15. CH4 1 97E 01 1 97E 01 C4 6 87E 21 6 78E 21,C2H6 1 45E 01 1 45E 01 C4N2 1 98E 27 1 95E 27. H2 8 95E 02 8 93E 02 C5 4 84E 30 4 75E 30,CO 4 48E 02 4 47E 02 C solid 4 89E 03 4 86E 03. Differences between values of product contents calculated by the both. programs remain small below 1 5, If the detonation parameters of an explosive are determined then calculation.
of the isentrope of expanding products is possible Every point on the isentrope. must fulfill a condition of constant entropy i e S const. The expansion isentrope for the detonation products of RDX from the. pressure at the CJ point to the atmospheric one was calculated It was assumed. that the composition of products is frozen when their temperature lowers to. 1800 K This value of the frozen temperature results from the theoretical. and experimental data presented in work 16 The results of calculation of the. isentrope are presented in Table 8 Differences between the values calculated by. the ZMWNI and CHEETAH codes are below 0 1,104 S Grys W A Trzci ski. Table 8 Comparison of the pressure values calculated in chosen points of. the isentrope of RDX detonation products by the use of the ZMWNI. and CHEETAH codes,ZMWNI CHEETAH,0 76 266513 70 266578 70. 1 00 115775 30 115748 20,2 20 13642 10 13637 60,2 41 10943 00 10951 60. 4 10 3380 70 3379 60,6 50 1408 80 1408 30,10 00 675 70 675 50. 20 00 231 10 231 10,40 00 85 30 85 30,80 00 32 60 32 60.
160 00 12 60 12 60, To solve a problem connected with the interaction of the explosion on the. surroundings expansion of the explosion products into air the explosion in water. or ground reflection of a detonation waves at a boundary with solids throwing. fragments forming a cumulative jet a knowledge of the equation of state for. the detonation products is necessary Universally used equation of this type was. suggested by Jones Wilkins and Lee JWL 12, The JWL equation is obtained from the expansion of internal energy in the. neighbourhood of an isentrope of the detonation products This isentrope has. the following form on the plain v p,p s Ae R1V Be R2V CV 1 1. where V v v0, Constants A B C R1 R2 and are most often determined empirically. A cylindrical test described in detail in Ref 18 is one of essential methods. of appointing them These constants can also be determined on the basis of. thermochemically calculated expansion isentrope The second option was applied. At the end some calculated detonation characteristics are compared with the experimental ones Keywords thermochemical codes energetic materials combustion explosion detonation Introduction Effective theoretical calculations of the detonation parameters and the chemical equilibrium composition of reaction products based on physical and chemical properties of an energetic material as

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